Question
Download Solution PDFIf the angle of elevation of the sun changes from 30° to 45° the length of the shadow of a pillar decreases by 20 meters. The height of the pillar is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:-
The angle of elevation of the Sun = 30o and 45o
Calculation:-
Let AB = h be the height of the pillar.
In Δ ABC
Tanθ = AB/BC = h/x
Tan45° = h/x
⇒ h = x - - - (i)
In Δ ABD
Tan30° = h/(x + 20)
⇒ 1√3 = h/(x + 20)
⇒ h = (x + 20)/√3 - - - - (ii)
From equations i and ii
⇒ (x + 20)/√3 = x
⇒ √3x = x + 20
⇒ √3x - x = 20
⇒ x(√3 - 1) = 20
⇒ x = 20/(√3 - 1)
We take the reciprocal method
⇒ x = 20(√3 + 1)/(√3 - 1)(√3 + 1)
⇒ x = 20(√3 + 1)/2
⇒ x = 10(√3 + 1)
As we know from the equation (i) h = x
Height = 10(√3 + 1)
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